In infinitely many steps I am using the sequence (displayed in bold) to create the list of natural numbers (001 = 01 = 1):(adsbygoogle = window.adsbygoogle || []).push({});

1.

...000000

...000001

...000010

...000011

...000100

...000101

...000110

...000111

...001000

...

2.

...000000

...000001

...000010

...000011

...000100

...000101

...000110

...000111

...001000

...

3.

...000000

...000001

...000010

...000011

...000100

...000101

...000110

...000111

...001000

...

In infinitely many steps I am using the same sequence to create a list of what I would call the binary complement of the natural numbers:

1.

...

...110111

...111000

...111001

...111010

...111011

...111100

...111101

...111110

...111111

2.

...

...110111

...111000

...111001

...111010

...111011

...111100

...111101

...111110

...111111

3.

...

...110111

...111000

...111001

...111010

...111011

...111100

...111101

...111110

...111111

I have displayed how to create two different lists of countably infinitely many lines. Is there a similar way to display how the same sequence can be used to create 2^ω which includes all infinite binary sequences?

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# Infinite Product

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